Probit method of cumulative distribution function determination of energetic sensitivity

ABSTRACT

Embodiments of the invention disclose the determination of the actual shape of a cumulative distribution function (CDF) for an energetic composition. Sensitivity tests and historical data are configured for input into an electronic processor. An energetic determination tool is configured to determine the actual shape of the CDF. The actual shape of the CDF is output in a tangible medium.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a non-provisional application, claiming the benefit of parentprovisional application No. 61/935,529 filed on Feb. 4, 2014, wherebythe entire disclosure of which is incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The invention described herein may be manufactured and used by or forthe government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

FIELD OF THE INVENTION

The invention generally relates to the determination of the sensitivityof energetic materials to explosive shock.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a system and its operational components forcumulative distribution function determination, according to someembodiments of the invention.

FIG. 1B is an exemplary flowchart illustrating tasks for simulating theactual shape of a cumulative distribution function, according to someembodiments of the invention.

FIG. 1C is an exemplary flowchart illustrating the tasks for cumulativedistribution function determination, according to some embodiments ofthe invention.

FIG. 2 illustrates a scatter plot of probability events (smallestextreme value) at a corresponding number of attenuator cards, a smallestextreme value CDF, according to some embodiments of the invention.

FIG. 3 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a Weibull CDF, according tosome embodiments of the invention.

FIG. 4 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a 3 parameter Weibull CDF,according to some embodiments of the invention.

FIG. 5 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, an exponential CDF, accordingto some embodiments of the invention.

FIG. 6 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a 2 parameter exponential CDF,according to some embodiments of the invention.

FIG. 7 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a normal CDF, according tosome embodiments of the invention.

FIG. 8 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a log normal CDF, according tosome embodiments of the invention.

FIG. 9 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a 3 parameter log normal CDF,according to some embodiments of the invention.

FIG. 10 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a logistic CDF, according tosome embodiments of the invention.

FIG. 11 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a log logistic CDF, accordingto some embodiments of the invention.

FIG. 12 illustrates a scatter plot of probability events P at acorresponding number of attenuator cards, a 3 parameter log logisticCDF, according to some embodiments of the invention.

It is to be understood that the foregoing general description and thefollowing detailed description are exemplary and explanatory only andare not to be viewed as being restrictive of the invention, as claimed.Further advantages of this invention will be apparent after a review ofthe following detailed description of the disclosed embodiments, whichare illustrated schematically in the accompanying drawings and in theappended claims.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Embodiments of the invention calculate the actual shape of a cumulativedistribution function (CDF) by conducting tests at predetermined levels,thereby allowing precise determination of the 50 percent sensitivitylevel and associated confidence interval.

For background, Bruceton analysis, also known as the “Up and Down Test”or “the staircase method,” relies upon two parameters: (1) stimulus and(2) step size. A stimulus, which is some form of energy depending onapplication-specific conditions, is provided to the sample, and theresults noted. When a positive result is noted, then the stimulus isdecremented by the step size. When a negative result occurs, thestimulus is increased. The test continues with each sample tested at astimulus 1 step up or down from the previous stimulus if the previousresult was negative or positive. For explosive sensitivity tests, a GapTest apparatus described in the above-mentioned documents usesattenuator cards with a standard explosive donor charge. Decreasing thenumber of attenuator cards increases the stimulus to the material undertest and likewise, increasing the number of attenuator cards decreasesthe stimulus to the material under test. The results are then tabulatedand analyzed via Bruceton analysis, a simple computation of sums thatcan be performed by pencil and paper providing estimates of the mean andstandard deviation. Confidence estimates are also produced.

The Cumulative Distribution Function (CDF) will in general be amonotonic function but not necessarily symmetric. The drawback with theBruceton method is that the results will be influenced by the shape ofthe CDF, the starting point of the test relative to the CDF, and thenumber of tests performed. Therefore, the Bruceton method would yieldthe most accurate result with a CDF that approaches a step function,centered about some value. As the shape of the CDF diverges from thisideal, the result will likewise decrease in accuracy.

Although embodiments of the invention are described in considerabledetail, including references to certain versions thereof, other versionsare possible. Examples of other versions include performing the tasks inan alternate sequence or hosting embodiments on different platforms.Therefore, the spirit and scope of the appended claims should not belimited to the description of versions included herein.

A person having ordinary skill in the art of statistics will recognizethat probit modeling is a type of regression where the dependentvariable takes one of two values. The model estimates probability thatan observation having certain characteristics will fall into one of thecategories (one of the two values). When estimated values greater than ½are treated as an observation into a predicated category, the probitmodel is a binary classification model.

Embodiments of the invention include calculating the actual shape of theCDF by conducting the tests at predetermined levels, thereby allowingprecise determination of the 50% sensitivity level and associatedconfidence interval. Embodiments of the invention are equally applicableto method and articles of manufacture embodiments. Article ofmanufacture embodiments are directed to non-transitory processorreadable medium(s) having stored thereon processor executableinstructions that, when executed by the processor(s), cause theprocessor to perform the process(es) described herein. The termnon-transitory processor readable medium include one or morenon-transitory processor-readable medium (devices, carriers, or media)having stored thereon a plurality of instructions, that, when executedby the electronic processor (typically a central processing unit—anelectronic circuit which executes computer programs, containing aprocessing unit and a control unit), cause the processor toprocess/manipulate/act on data according to the plurality ofinstructions (defined herein using the process/function form). Thenon-transitory medium can be any non-transitory processor readablemedium (media), including, for example, a magnetic storage media,“floppy disk,” CD-ROM, RAM, a PROM, an EPROM, a FLASH-EPROM, NOVRAM, anyother memory chip or cartridge, a file server providing access to theprograms via a network transmission line, and a holographic unit. Ofcourse, those skilled in the art will recognize that many modificationsmay be made to this configuration without departing from the scope.

In some system embodiments, the electronic processor is co-located withthe processor readable medium. In other system embodiments, theelectronic processor is remotely located from the processor readablemedium. It is noted that the steps/acts/processes/tasks described hereinincluding the figures can be interpreted as representing data structuresor sets of instructions for causing the computer readable medium toperform the step/act/process.

Certain embodiments of the invention may take the form of non-transitoryprocessor readable mediums having computer-usable/readable programinstructions embodied in the medium. Any suitable computer readablemedium may be utilized including either computer readable storage media,such as, for example, hard disk drives, CD-ROMs, optical storagedevices, or magnetic storage devices, or a transmission media, such as,for example, those supporting the internet or intranet.

Computer-usable/readable program instructions for carrying outoperations of embodiments of the invention may be written in an objectoriented programming language such as, for example, Python, VisualBasic, or C++. However, computer-usable/readable program instructionsfor carrying out operations of embodiments of the invention may also bewritten in conventional procedural programming languages, such as, forexample, the C or C# programming languages or an engineering prototypinglanguage such as, for example, MATLAB®. However, the concepts may bereplicated for many platforms provided that an appropriate compiler isused.

The computer-usable/readable program instructions may execute entirelyon the user's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer. In the latter scenario, theremote computer may be connected to the user's computer through a localarea network (LAN) or a wide area network (WAN), or the connection maybe made to an external computer (for example, through the Internet usingan Internet Service Provider or any other method known in the art).

Embodiments of the invention are described in part below with referenceto flow chart illustrations and/or block diagrams of methods andcomputer program products according to embodiments of the invention. Itwill be understood that each block of the flow chart illustrationsand/or block diagrams, and combinations of blocks in the flow chartillustrations and/or block diagrams, can be implemented by computerprogram instructions. These computer program instructions may beprovided to a processor of a general purpose computer, special purposecomputer, or other programmable data processing apparatus to produce amachine, such that the instructions, which execute via the processor ofthe computer or other programmable data processing apparatus, createmeans for implementing the functions/acts specified in the flow chartand/or block diagram block or blocks.

These computer program instructions may also be stored in acomputer-readable memory, including RAM, that can direct a computer orother programmable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instructions thatimplement the function/act specified in the flow chart and/or blockdiagram block or blocks.

These computer program instructions may also be loaded onto a computeror other programmable data processing apparatus to cause a series ofoperational tasks to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions that execute on the computer or other programmableapparatus provide tasks for implementing the functions/acts specified inthe flow chart and/or block diagram block or blocks.

In the accompanying drawings, like reference numbers indicate likeelements. FIG. 1A illustrates a system and its operational componentsfor cumulative distribution function determination of energeticsensitivity. Reference character 10 depicts a system of embodiments ofthe invention. The system 10, may also be referred to as an apparatus,method, or a combination of both apparatus and method for shorthandpurposes, without detracting from the merits or generality ofembodiments of the invention.

Embodiments of the invention generally relate to a system fordetermining the actual shape of a cumulative distribution function (CDF)for an energetic composition. The system 10 includes at least oneelectronic processor having a central processing unit 12. The centralprocessing unit (CPU), and computer memory are electrically connected tothe computer's motherboard. A graphics processing unit (GPU) may also beemployed in some embodiments of the invention are in those embodiments,the GPU is also electrically connected with the motherboard. In someapplications, depending on the verification requirements, a visualverification by a user may be important to provide an additional layerof validation before acting on the processing result.

A grouping of sensitivity tests at particularized segments andsensitivity test data 14 associated with said grouping of sensitivitytests data is configured for input into the electronic processor 12.Historical pelletized explosive test data 16 corresponding to previoustest data performed on the energetic composition is configured for inputto the electronic processor 12.

An energetic determination tool 18 is associated with the electronicprocessor 12. The energetic determination tool 18 is configured todetermine the actual shape of a cumulative distribution function (CDF)associated with the energetic composition. The determination of theactual shape of the CDF allows for more accurate determination of the 50percent energetic sensitivity level of the energetic composition. Atleast one device 20 is associated with the electronic processor 12 andis configured to output the actual shape of the CDF in a tangible mediumsuch as a visual display screen. The actual shape of the CDF would bedisplayed, for example, on an x-y axis plot with the x-axis depicting arange of the particularized segments, which are the number of attenuatorcards from zero to about 300 cards. The y-axis depicts sensitivityprobabilities of the energetic composition. Although numerous othertangible mediums for output include hard copy prints as well as othermedia configured to use output from embodiments of the invention.

FIGS. 1B & 1C are equally applicable to methods and articles ofmanufacture associated with embodiments of the invention. Referencecharacters 100 and 150 are used to refer to both methods and articles ofmanufacture in FIGS. 1B & 1C, respectively.

Referring to both FIGS. 1A & 1C, the energetic determination tool is anon-transitory electronic-processor-readable medium having a pluralityof electronic processor executable instructions stored thereon. Theexecutable instructions when executed by the electronic processor 12,causes the processor to perform several tasks to obtain the actual shapeof the cumulative distribution function (CDF) for the energeticcomposition. The electronic processor 12 includes a data storage device.

As shown in FIG. 1C, as depicted in task 152, historical pelletizedexplosive test data is input into an electronic processor. In task 154,a range of sensitivity values is determined for the energeticcomposition. The range is selected based on the historical pelletizedexplosive test data for similar energetic composition formulations. Therange is selected by the user or in some embodiments, the electronicprocessor executable instructions select the range based on thehistorical pelletized explosive test data. The range is bounded bysensitivity endpoints.

In task 156, the sensitivity values are divided into at least threesegments between the sensitivity endpoints. The segments may be equallyspaced or not equally spaced. The segments correspond to predeterminedsensitivity levels based on the historical pelletized explosive data. Insome embodiments, the selected number of segments is three. In otherembodiments, the selected number of segments is four.

In task 158, sensitivity tests are electronically performed simulationsat each of the segments (at least three segments). The target number oftests at each of the segments is about ten tests per segment. Of course,it is understood that more than or less than ten tests per segment maybe performed based on historical data. The sensitivity tests yieldsensitivity test data. The sensitivity test data iselectronically-recorded and stored in memory associated with theelectronic processor 12 (task 160).

In task 162, the sensitivity test data is electronically analyzed by theelectronic processor 12. The analysis in task 162 is a probit analysisthat stacks response data with a corresponding stimulus level for eachresponse entry. The probit analysis is performed by stacking allresponse data in one column with corresponding stimulus level for eachresponse entry in an adjacent column. The number of events is thenconverted to a percentage. An example of converting the stimulus to apercent would be performing statistical analysis by entering the columnwith the particular data into a variables box, such as a first windowsbox and the column with the stimulus levels into a second windows box.Statistical variance and mean can be calculated.

The response data occurs where detonation is exhibited in the energeticcomposition. Probability distributions can be examined includingsmallest extreme value, Weibull, Normal, Log normal, logistic, or loglogistic, that possess a correlation coefficient closest to one (1). Theprobit analysis is performed with the selected distribution. Responseand stimulus levels are processed. This results in a probability plotshowing the fitted percent probability versus stimulus level, thestimulus levels relative to the fitted probability, and the confidenceintervals associated with the fitted probability.

Task 164 electronically fits a best fit curve through data pointscorresponding to the proportion of detonation events of the energeticcomposition. The best fit curve is output in task 166 in the tangiblemedium described earlier, such as on the visual display screen 20.Outputting of the best fit curve includes visually displaying the fittedpercent probability versus stimulus level, stimulus levels relative tothe fitted probability, and the confidence intervals associated with thefitted probability.

In yet another embodiment, as depicted in FIG. 1B, depicted as referencecharacter 100, a method for simulating the actual shape of a cumulativedistribution function (CDF) that describes the energetic sensitivity ofan energetic composition is shown. The method lends itself to validatingtest methods and previously performed analysis of the energeticcomposition. The output produced by the method determines the 50 percentenergetic sensitivity level of the energetic composition.

Historical pelletized explosive test data is input into the electronicprocessor. The grouping of sensitivity tests at particularized segmentsand the patterned sensitivity test data is input into the electronicprocessor (task 102). The patterned sensitivity test data has theparameters of a plurality of attenuator cards ranging from zero to 300attenuator cards and an event probability value corresponding to eachattenuator card in the plurality of attenuator cards. The range ofsensitivity values is defined from zero to 300 attenuator cards.Sensitivity endpoints occur at both zero and 300 attenuator cards. Therange of sensitivity values is divided into at least three segmentsbetween the sensitivity endpoints. The three segments correspond to thepredetermined sensitivity levels based on the historical pelletizedexplosive data.

In task 104, a distribution function is selected for the patternedsensitivity test data. Some distribution functions that can be selectedare discussed and illustrated in detail in FIGS. 2 through 12. An eventprobability is determined for the distribution function (task 106). Intask 108, cumulative distribution function (CDF) data is generated thatcorresponds to the event probability. Task 110 determines a detonationCDF of the generated CDF data. A desired 50 percent energeticsensitivity level of the detonation CDF is selected in task 112. Thedesired 50 percent energetic sensitivity level corresponds to at leastthree segments for random data creation. The random data creation isuseful for simulating processes.

In task 114, a number of simulated sensitivity test experiments aredetermined. The simulated sensitivity test experiments correspond toeach of the at least three segments. The number of simulated sensitivitytest experiments are input into the electronic processor. The electronicprocessor is instructed to electronically simulate the sensitivity teststhe determined number of times at each of the at least three segments.The simulated sensitivity test experiments produce simulated sensitivitytest data that is electronically recorded and stored in the electronicmemory associated with the electronic processor.

The simulated test data is converted (changed), if necessary, from atext to a numeric data format. The simulated sensitivity test data iselectronically analyzed. The analysis provides response data points. Thedata response data points correspond to a proportion of detonationevents at the simulated sensitivity tests at each of the at least threesegments. Response data is stacked with a corresponding stimulus levelfor each response entry. The response data is the response data pointscorresponding to the proportion of detonation events. The stimulus levelis energy applied to the energetic composition. A best fit curve iselectronically fit through the response data points. The best fit curveis defined as the actual shape of the CDF.

The best fit curve is output in the tangible medium. Included in theanalysis is the automated of corresponding attenuator card valuescorresponding to the 50 percent energetic sensitivity value from thebest fit curve. The card value (the number of cards at which the 50percent point is located) is also produced as output (tasks 116 through122).

Scenarios can, of course, occur when historical pelletized explosivetest data is not available for a particular energetic composition. Inscenarios such as those, physical testing is performed on the energeticcomposition. The physical testing produces pelletized test results forthe energetic composition. The pelletized test results are then labeledand stored as historical pelletized test data and configured for inputinto the electronic processor 12.

The physical testing performed on the energetic composition whenhistorical pelletized explosive test data does not exist is a gap test.A gap test is conducted with a first endpoint of zero attenuator cardsand a second endpoint of three inches of cards. The first and secondendpoints are defined as extremes. The attenuator cards are about 0.01inches thick and are constructed of Plexiglass® or similar material. Onehaving ordinary skill in the art will recognize that Plexiglass® is apoly methyl methacrylate (PMMA) and is a transparent thermoplastic,sometimes called acrylic glass, that is a lightweight orshatter-resistant alternative to glass.

The concept is to fill up space with the cards until detonation of theenergetic composition occurs. All the predetermined levels of testingare then conducted using the gap test. The data is obtained and then thebest fit curve procedure (the output), as described above is performed.When an event (detonation of the energetic composition) is not recordedat zero gap (zero attenuator cards) or an event is recorded at threeinches of gap (300 attenuator cards), the test is defined asinappropriate because the data is not actionable because it is locatedat the extremes.

For the physical testing, the samples are prepared by being pressed intopellets to test at regions between the extremes. A target number oftests is one test at about every 0.3 inches of gap between the first andsecond endpoint (between zero and three inches of attenuator cards).When an event is not recorded at zero gap or an event is recorded atthree inches of gap, the test is defined as inappropriate. A range isselected between gap values where an event is first noted and whereevents occur repeatedly.

FIGS. 2 through 12

Significant modeling was performed on embodiments of the invention.FIGS. 2 through 12 illustrate some of the modeling, as illustrated onthe visual display screen or hardcopy printouts. The curves shown inFIGS. 2 through 12 have different underlying probability distributions.Different energetic composition materials behave differently. The CDF ischosen that most closely mimics the energetic material of interest. Themodeling includes substantial statistical analysis to determine eventprobabilities for increasing attenuator card values according to therelationship of: event probability=1−CDF. The particular CDF values areobtained according to individualized statistical analysis basedhistorical data and the number of parameters.

The embodiments of the invention fit a curve to data points and can thenread an exact 50 percent sensitivity level (the number of attenuatorcards at a 50 percent probability). For FIGS. 2 through 12, the x-axisrepresents the attenuator cards and the y-axis represents theprobability values from 0 to 1.0 (0 percent to 100 percent). Each time asimulation is performed, a curve is fit to the respective data pointswhich allows the determination of the 50 percent sensitivity level (the50 percent probability) at that simulation. This allows for multiplesimulations to be performed.

The modeling employs unitless parameter numbers for shape, threshold,and scale, according to which distribution is being modeled. A scaleexample includes standard deviation. A threshold example includes mean.Parametric probability distributions have the properties of shape,scale, and location. Shape, as the name implies, will fundamentallychange the shape of the distribution. The modeled distributions are asshown in FIGS. 2 through 12.

For some corresponding event probabilities of increasing card values(task 106), the CDF is determined by

${CDF} = {e^{- {(\frac{x - {location}}{scale})}}.}$The larger the scale, the more gradual the CDF appears betweenprobabilities of one and zero. As an example, trying a scale of 10 tostart, the location is calculated bylocation=scale(−ln(−ln(0.5))+desired 50% point).

FIG. 2 illustrates a smallest extreme value CDF, as depicted byreference character 200. The smallest extreme value CDF is determined by

${CDF} = {e^{- {(\frac{x}{scale})}^{shape}}.}$The larger the shape, the less gradual the CDF appears between theprobabilities of one and zero. Trying a shape of 10 to start, the scaleis calculated byscale=e ^(ln(ln(desired 50% point)-ln(-ln(0.5))/shape)).

FIG. 3 illustrates a Weibull CDF, as depicted by reference character300. The Weibull CDF is determined by

${CDF} = {e^{- {(\frac{x - {threshold}}{scale})}^{shape}}.}$The larger the shape, the less gradual the CDF appears between theprobabilities of one and zero. Trying a shape of 10 to start, the scaleis calculated byscale=e ^(ln(ln(desired 50% point-threshold)-ln(-ln(0.5))/shape)).

FIG. 4 illustrates a 3 parameter Weibull CDF, as depicted by referencecharacter 400. The 3 parameter Weibull CDF is determined by

${CDF} = {e^{- {(\frac{x}{scale})}}.}$The larger the scale, the more gradual the slope of the function as itapproaches 0. The scale is calculated by

${scale} = {- {\frac{\left( {{desired}\mspace{14mu} 50\%\mspace{14mu}{point}} \right)}{\ln({.5})}.}}$

FIG. 5 illustrates an exponential CDF, as depicted by referencecharacter 500. The exponential CDF is determined by

${CDF} = {e^{- {(\frac{x - {threshold}}{scale})}}.}$scale, the more gradual the slope of the function as it approaches 0.The scale is calculated by

${scale} = {- {\frac{\left( {{{desired}\mspace{14mu} 50\%\mspace{14mu}{point}} - {threshold}} \right)}{\ln({.5})}.}}$

FIG. 6 illustrates a 2 parameter exponential CDF, as depicted byreference character 600. The 2 parameter exponential CDF is determinedusing the complementary error function by

${CDF} = {1 - {(0.5){{{erfc}\left( {- \left( \frac{x - {location}}{\sqrt{2}\mspace{14mu}{scale}} \right)} \right)}.}}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the desired 50% point is the location value.

FIG. 7 illustrates a normal CDF, as depicted by reference character 700.The normal CDF is also determined using the complementary error functionby

${CDF} = {1 - {(0.5){{{erfc}\left( {- \left( \frac{{\ln(x)} - {location}}{\sqrt{2}\mspace{14mu}{scale}} \right)} \right)}.}}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the location is calculated to be ln(desired 50% point). The argument ofthe natural logarithm must be greater than zero. Therefore, attenuatorcard values are greater than zero.

FIG. 8 illustrates a log normal CDF, as depicted by reference character800. The log normal CDF is also determined using the complementary errorfunction by

${CDF} = {1 - {(0.5){{{erfc}\left( {- \left( \frac{{\ln\left( {x - {threshold}} \right)} - {location}}{\sqrt{2}\mspace{14mu}{scale}} \right)} \right)}.}}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the location is calculated to be ln(desired 50% point−threshold). Theargument of the natural logarithm must be greater than zero. Therefore,attenuator card values are greater than zero.

FIG. 9 illustrates a 3 parameter log normal CDF, as depicted byreference character 900. The 3 parameter log normal CDF is determined by

${CDF} = {1 - {\left( \frac{1}{1 + e^{{- {({x - {location}})}}/{scale}}} \right).}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the desired 50 percent point is the location value.

FIG. 10 illustrates a logistic CDF, as depicted by reference character1000. The logistic CDF is determined by

${CDF} = {1 - {\left( \frac{1}{1 + e^{- {(\frac{{\ln{(x)}} - {location}}{scale})}}} \right).}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the location is calculated to be ln(desired 50% point). The argument ofthe natural logarithm must be greater than zero. Therefore, attenuatorcard values are greater than zero.

FIG. 11 illustrates a log logistic CDF, as depicted by referencecharacter 1100. The log logistic CDF is determined by

${CDF} = {1 - {\left( \frac{1}{1 + e^{- {(\frac{{\ln{({x - {threshold}})}} - {location}}{scale})}}} \right).}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the location is calculated to be ln(desired 50% point−threshold). Theargument of the natural logarithm must be greater than zero. Therefore,attenuator card values are greater than zero.

FIG. 12 illustrates a 3 parameter log logistic CDF, as depicted byreference character 1200. The 3 parameter log logistic CED is determinedby

${CDF} = {1 - {\left( \frac{1}{1 + e^{- {(\frac{{\ln{({x - {threshold}})}} - {location}}{scale})}}} \right).}}$The larger the scale, the more gradual the CDF appears between theprobabilities of one and zero. Trying a scale of location/10 to start,the location is calculated to be ln(desired 50% point−threshold).

While the invention has been described, disclosed, illustrated and shownin various terms of certain embodiments or modifications which it haspresumed in practice, the scope of the invention is not intended to be,nor should it be deemed to be, limited thereby and such othermodifications or embodiments as may be suggested by the teachings hereinare particularly reserved especially as they fall within the breadth andscope of the claims here appended.

What is claimed is:
 1. A system for determining sensitivity of at leastone energetic composition material to explosive shock using an energeticdetermination tool to determine an actual shape of a cumulativedistribution function (CDF) for said at least one energetic compositionmaterial, comprising: at least one electronic processor having a centralprocessing unit (CPU); a grouping of sensitivity tests at particularizedsegments and patterned sensitivity test data associated with saidgrouping of sensitivity tests, said grouping of sensitivity tests atparticularized segments and said patterned sensitivity test dataconfigured for input to said at least one electronic processor;historical pelletized explosive test data corresponding to previous testdata performed on said at least one energetic composition material, saidhistorical pelletized explosive test data configured for input to saidat least one electronic processor; an energetic determination toolassociated with said at least one electronic processor, wherein saidenergetic determination tool is configured to determine an actual shapeof a cumulative distribution function (CDF); and at least one deviceassociated with said at least one electronic processor configured tooutput in a tangible medium the actual shape of said CDF; wherein saidenergetic determination tool is a non-transitoryelectronic-processor-readable medium having a plurality of electronicprocessor executable instructions stored thereon, that when executed bysaid at least one electronic processor, causes said at least oneelectronic processor to: input said historical pelletized explosive testdata into said at least one electronic processor; determine a range ofsensitivity values of said at least one energetic composition material,said range based on said historical pelletized explosive test data;wherein said range is bounded by sensitivity endpoints; divide saidrange of sensitivity values into at least three segments between saidsensitivity endpoints, said at least three segments corresponding topredetermined sensitivity levels based on said historical pelletizedexplosive data; electronically simulate sensitivity tests at each ofsaid at least three segments, said sensitivity tests producingsensitivity test data; electronically record said sensitivity test dataand store said sensitivity test data in said electronic memory;electronically determine a CDF by analyzing said sensitivity test data,wherein said analysis provides response data points, said response datapoints corresponding to a proportion of detonation events at saidsimulated sensitivity tests at each of said at least three segments;electronically fit a best fit curve through said response data points,wherein said best fit curve is defined as the actual shape of said CDF;output said best fit curve in said tangible medium; and obtain said atleast one energetic composition material corresponding to the actualshape of said CDF.
 2. The system according to claim 1, wherein when saidhistorical pelletized explosive test data is not available, performphysical testing on said at least one energetic composition material,said physical testing producing pelletized results for said at least oneenergetic composition material, said pelletized results being labeled ashistorical pelletized test data and configured for input to said atleast one electronic processor, wherein the performance of physicaltesting, further comprising: conducting a gap test with a first endpointof zero attenuator cards and a second endpoint of three inches of cards,where said first and said second endpoints are defined as extremes; whenan event is not recorded at zero gap or an event is recorded at threeinches of gap, defining the test as inappropriate; preparing samples totest at regions between said extremes, wherein a target number of testsis one test at every 0.3 inches of gap between said first and saidsecond endpoint; and selecting a range to pick for said test between gapvalues where an event is first noted and where events occur repeatedly.3. The system according to claim 1, said analyzing task furthercomprising: stacking response data with a corresponding stimulus levelfor each response entry, wherein said response data are said responsedata points corresponding to said proportion of detonation events,wherein said stimulus level is energy applied to said at least oneenergetic composition material; converting said proportion of detonationevents at each of said corresponding stimulus level to a percentage;identifying a probability distribution that best describes said responsedata points; determining a probabilistic model for said fitting a bestfit curve task, said determination based on said historical pelletizedexplosive data; and performing a probit analysis of said identifiedprobability distribution that best describes said response data points.4. The system according to claim 3, wherein said outputting said bestfit curve task further comprising visually displaying a fitted percentprobability versus stimulus level, stimulus levels relative to thefitted probability, and the confidence intervals associated with thefitted probability.
 5. The system according to claim 1, wherein said atleast three segments is three segments.
 6. The system according to claim1, wherein said at least three segments is four segments.
 7. The systemaccording to claim 1, wherein said tangible medium is a visual displayscreen.
 8. A method for determining sensitivity of at least oneenergetic composition material to explosive shock using an energeticdetermination tool to determine an actual shape of a cumulativedistribution function (CDF) of said at least one energetic compositionmaterial using an electronic processor having a central processing unit(CPU) and a graphics processing unit (GPU) associated with said CPU,said method comprising: providing a grouping of sensitivity tests atparticularized segments and patterned sensitivity test data associatedwith said grouping of sensitivity tests data, said grouping ofsensitivity tests at particularized segments and said patternedsensitivity test data configured for input to at least one electronicprocessor; providing historical pelletized explosive test data for saidat least one energetic composition material, said historical pelletizedexplosive test data corresponding to previous tests performed on said atleast one energetic composition material, said historical pelletizedexplosive test data configured for input to said at least one electronicprocessor; providing an energetic determination tool associated withsaid at least one electronic processor, wherein said energeticdetermination tool is configured to determine the actual shape of acumulative distribution function (CDF); inputting said patternedsensitivity test data into said at least one electronic processor;inputting said historical pelletized explosive test data into said atleast one electronic processor; determining a range of sensitivityvalues of said at least one energetic composition material based on saidhistorical pelletized explosive test data, wherein said range is boundedby sensitivity endpoints; dividing said range of sensitivity values intoat least three segments between said sensitivity endpoints, said atleast three segments corresponding to predetermined sensitivity levelsbased on said historical pelletized explosive data; simulatingsensitivity tests at each of said at least three segments, saidsensitivity tests producing sensitivity test data; recording saidsensitivity test data and storing said sensitivity test data in saidelectronic memory; electronically determining a CDF by analyzing saidsensitivity test data, wherein said analysis provides response datapoints, said response data points corresponding to a proportion ofdetonation events at said simulated sensitivity tests at each of said atleast three segments; electronically fitting a best fit curve throughsaid response data points, wherein said best fit curve is defined as theactual shape of said CDF; outputting said best fit curve in a tangiblemedium; and obtaining said at least one energetic composition materialcorresponding to the actual shape of said CDF.
 9. The method accordingto claim 8, wherein when historical data is not available, said methodcomprising performing physical testing on said at least one energeticcomposition material, said physical testing producing pelletized resultsfor said at least one energetic composition material, said pelletizedresults being labeled as historical pelletized test data and configuredfor input to said at least one electronic processor, wherein theperformance of physical testing, further comprising: conducting a gaptest with a first endpoint of zero attenuator cards and a secondendpoint of three inches of cards, where said first and said secondendpoints are defined as extremes; when an event is not recorded at zerogap or an event is recorded at three inches of gap, defining the test asinappropriate; preparing samples to test at regions between saidextremes, wherein a target number of tests is one test at every 0.3inches of gap between said first and said second endpoint; and selectinga range to pick for said test between gap values where an event is firstnoted and where events occur repeatedly.
 10. The method according toclaim 8, said analyzing task, further comprising: stacking response datawith a corresponding stimulus level for each response entry, whereinsaid response data are said response data points corresponding to saidproportion of detonation events, wherein said stimulus level is energyapplied to said at least one energetic composition material; convertingsaid proportion of detonation events at each of said correspondingstimulus level to a percentage; identifying a probability distributionthat best describes said response data points; determining aprobabilistic model for said fitting a best fit curve task, saiddetermination based on said historical pelletized explosive data; andperforming a probit analysis of said identified probability distributionthat best describes said response data points.
 11. The method accordingto claim 10, wherein said outputting said best fit curve task furthercomprising visually displaying a fitted percent probability versusstimulus level, stimulus levels relative to the fitted probability, andthe confidence intervals associated with the fitted probability.
 12. Themethod according to claim 8, wherein said at least three segments isthree segments.
 13. The method according to claim 8, wherein said atleast three segments is four segments.
 14. The method according to claim8, wherein said tangible medium is a visual display screen.